Two-dimensional Euler flows in slowly deforming domains

Mathematics – Analysis of PDEs

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

38 pages, 4 figures

Scientific paper

We consider the evolution of an incompressible two-dimensional perfect fluid as the boundary of its domain is deformed in a prescribed fashion. The flow is taken to be initially steady, and the boundary deformation is assumed to be slow compared to the fluid motion. The Eulerian flow is found to remain approximately steady throughout the evolution. At leading order, the velocity field depends instantaneously on the shape of the domain boundary, and it is determined by the steadiness and vorticity-preservation conditions. This is made explicit by reformulating the problem in terms of an area-preserving diffeomorphism $\gL$ which transports the vorticity. The first-order correction to the velocity field is linear in the boundary velocity, and we show how it can be computed from the time-derivative of $\gL$. The evolution of the Lagrangian position of fluid particles is also examined. Thanks to vorticity conservation, this position can be specified by an angle-like coordinate along vorticity contours. An evolution equation for this angle is derived, and the net change in angle resulting from a cyclic deformation of the domain boundary is calculated. This includes a geometric contribution which can be expressed as the integral of a certain curvature over the interior of the circuit that is traced by the parameters defining the deforming boundary. A perturbation approach using Lie series is developed for the computation of both the Eulerian flow and geometric angle for small deformations of the boundary. Explicit results are presented for the evolution of nearly axisymmetric flows in slightly deformed discs.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Two-dimensional Euler flows in slowly deforming domains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Two-dimensional Euler flows in slowly deforming domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Two-dimensional Euler flows in slowly deforming domains will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-350807

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.